On the basis of their language, content, and other factors, the Pastoral Epistles are today widely regarded as not having been written by the Apostle Paul, but after his death. (Although the Second Epistle to Timothy is sometimes thought to be more likely than the other two to have been written by Paul.) Critics examining the texts fail to find their vocabulary and literary style similar to Paul's unquestionably authentic letters, fail to fit the life situation of Paul in the epistles into Paul's reconstructed biography, and identify principles of the emerged Christian church rather than those of the apostolic generation.

One of the early critiques of the letters point to the large number of hapax legomenon found in them compared to the rest of Pauline corpus. But it seems that analysis has been shown to be flawed.

More difficult to me are passages like:

(No longer drink only water, but use a little wine for the sake of your stomach and your frequent ailments.)—1st Timothy 5:23 (ESV)

and:

O Timothy, guard the deposit entrusted to you. Avoid the irreverent babble and contradictions of what is falsely called “knowledge,” for by professing it some have swerved from the faith.
Grace be with you.—1st Timothy 6:20-21 (ESV)

and:

When I send Artemas or Tychicus to you, do your best to come to me at Nicopolis, for I have decided to spend the winter there. Do your best to speed Zenas the lawyer and Apollos on their way; see that they lack nothing. And let our people learn to devote themselves to good works, so as to help cases of urgent need, and not be unfruitful.
All who are with me send greetings to you. Greet those who love us in the faith.
Grace be with you all.—Titus 3:12-15 (ESV)

Quite personal and specific instructions are sprinkled throughout the Pastorals, which is one of the very reasons they are called "pastoral". So under what scenario could these fairly early Christian texts be accepted as authentically from Paul if they were written by someone else?

2 Answers
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I'm going to address your direct question of how a text could be accepted as Pauline if Paul didn't write it. I won't go into the specifics of the arguments for or against Pauline authorship of the Pastorals.

Of these, only the last would not be considered authentic in ancient times. That leaves considerable leeway for another writer's words to be accepted as Pauline.

And in fact, both Luke/Acts and Hebrews were included in the canon on Paul's authority, because the authors were believed to have been disciples of Paul. So in that sense, Luke/Acts and Hebrews were considered authentically Pauline even though they were written by someone else.

We also see, in the majority of Paul's letters, at least one coauthor. We don't know how much input the coauthors had into the content.

Furthermore, several of Paul's letters include a personal note written by Paul's own hand (see 1 Corinthians 16:21, Galatians 6:11, 2 Thessalonians 3:17, Colossians 4:18, Philemon 19), implying that the rest of the letter was written by an amanuensis. Again we don't know how much input the amanuensis had into the actual words of the document.

All this just underscores the difficulty in using vocabulary analysis to determine the authenticity of the Pastoral Epistles.

Acceptance of the Pastorals

What we do know, however, is that the early church universally recognized the Pastorals as authoritative, and we have a good idea of the criteria they used. The Muratorian Canon which possibly dates as early as 170. It lists the nine letters of Paul to seven churches, then adds:

[Paul also wrote] out of affection and love one to Philemon, one to Titus, and two to Timothy; and these are held sacred in the esteem of the Church catholic for the regulation of ecclesiastical discipline.

The Muratorian Canon also mentions "one to the Laodiceans, another to the Alexandrians" which were rejected by the church as forgeries, as these letters supported the dualism taught by Marcion. The same text also praises the worthiness of a text known as the Shepherd of Hermas, but excludes it from the canon due to its having been written after the age of the Apostles.

The Gospel of Luke was accepted on Paul's authority:

Luke, the well-known physician, after the ascension of Christ, when Paul had taken with him as one zealous for the law, composed it in his own name, according to [the general] belief. Yet he himself had not seen the Lord in the flesh; and therefore, as he was able to ascertain events, so indeed he begins to tell the story from the birth of John.

However, the letter to the Hebrews was not yet associated with Paul.

From this we can infer that the early Christians a) agreed the Pastorals were written during Apostolic times, b) saw nothing in the Pastorals going against Paul's teaching, and c) accepted Paul's name at the top of the letters.

Of the five types of authorship listed above, these criteria rule out #5, assuming we can trust the church's judgment. That still leaves options for the Pastorals to have been physically penned by someone other than Paul and still accepted by the church as authentic.

Lots of good information here but I would avoid painting early Christian canonical thoughts in such broad strokes just based on the Muratorian canon. Other second century/early third century discussions make it clear that things weren't settled. You can at least say that at least part of the Roman Christian community accepted them as Pauline.
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MalliochApr 3 '12 at 21:14

I'll try to add more early church references; while the canon wasn't fully settled until the 4th century, the 13 letters with the name Paul at the top were not disputed.
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Bruce AldermanApr 3 '12 at 21:21

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I don't know of anyone saying that they weren't Pauline, so no dispute there. In leau of many early church lists, a lot of this same data could be gathered just by seeing which books were quoted as authoritative and assumed to be by Paul by which fathers. Of course I say "just", but that's a pretty monumental task. This kind of wide-sweeping data would be even stronger evidence than a canon list, but not nearly as convenient to reference :)
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MalliochApr 3 '12 at 21:45

@Mallioch, one of my professors at AGTS did something like that for his doctoral thesis. It was huge.
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Frank LukeApr 4 '12 at 17:49

Though I wouldn't argue for these being un-pauline, the scenario is quite plausible even if I don't find the arguments convincing.

As you mention, language is often brought up as an argument. I've seen a few decent refutations of this arguments both from a statistically and methodologically, so I find it unconvincing. But people still repeat it as a reason. I find this argument problematic for the following reasons:

Because these letters were more personal, written to individuals, their language will naturally be a bit different than letters written to churches. One paper read at a SBL annual meeting a few years ago claimed that if you take out the words and grammar that are particular to this change of address, the letters fit more easily into Paul's normal word choices.

We have very little correspondence by Paul. Statistics based on word counts, syntactical choices etc. is simple on shady ground. Especially since...

The whole amanuensis angle on Paul's letters really casts a great deal of doubt on word statistics. There are clear indications from Paul's letters that he used an amanuensis at times. How much freedom was the amanuensis given? If a good deal in either the case of the pastorals or the other letters, much based on word statistics must be thrown out.

Another common one I've heard is that it assumes a church structure later than Paul's time. Some find the overseer/deacon split to be a bit too developed for the period of the church before Paul's death, so they must have been written by earnest disciples of Paul to settle issues within the church in a way that Paul would have approved. Or at least that is how the argument goes. I also don't find this convincing.

According to Acts (e.g. 20:17), elders/overseers/bishops and deacons clearly already existed in Paul's time. The idea of the elder would have naturally carried over from Judaism, so I would think that it would have been surprising if this wasn't the case. Of course some push Acts to way later and might argue that this is also an anachronism. This makes me wonder how many things we have to push to a later date just so we can argue that other things are late. Eventually we'll have most things pushed to the second century and we'll have almost nothing from the first. At some point you have to wonder how much hypothesis you can build on and still be sure of much.

As a corollary, this is frequently done with Christology. "High" Christology comes late, some say. But the Christology in the undisputed Pauline's in incredibly high if you read the signs right, and those are quite early.

So I don't find these arguments particularly convincing. However, that letters could falsely be attributed is plausible. Assuming for the sake of argument that the letters were pseudonymous, they could be distributed in areas that would not have enough first-hand knowledge to refute the authorship (e.g., perhaps you wouldn't distribute Titus in Crete at first, and might wait till Titus is dead). As use spreads, people start to assume that it was from Paul and by the late first/early second century, no one is alive who could effectively refute the attribution. This strikes me as very plausible. But plausibility and likelihood are very different things. Since I don't think any of the arguments are compelling, I think it needs to remain a theory, but nothing more.

Good call on the difference between plausibility and likelihood. (+1) But it seems to me that a pseudonymous author would do a better job of matching Paul's style if they were purposefully trying to pass them off as Paul's. I mean, why not write to a church rather than an individual like almost all of Paul's letters?
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Jon Ericson♦Apr 2 '12 at 16:20

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I think that's a valid point. With the exception of Philemon, all the other letters are to churches, so you would think they would stick with that. Of course that's what they argue for Colossians, and argue partly because the language style and vocabulary is so similar (sigh) to Ephesians. One author I read argued that the pseudonymous author switched to a personal tone just to sound more convincing. I personally find your point more compelling. This kind of thing has to be a case of cumulative evidence but there are too many "what if's" in these for them to be compelling to me.
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MalliochApr 2 '12 at 17:17